Although tones, chords and rhythms of music easily appear as pieces of a mathematical system, few see math as music. Any connection between them might seem coincidental and deserving of little more than passing interest relative to measurable educational outcomes.
We understand aspiring musicians practice printed music until they can play the notes and eventually feel the piece. At the same time, we expect math students to work through problems with reliably mechanical steps, executing them on the way to right or wrong answers as if this linear approach to mathematics is more deserving of our attention.
Nobody looks outside of math for a solution when the focus is on improving standardized test scores. Feeling and expressing does not have any place in our view of quantifiable proficiency. Theory supports moving past this limiting assumption, however. Research shows that joining music and math at many educational levels extends the benefits of listening, singing and playing an instrument beyond performance and entertainment.
Music study correlates with higher levels of mathematical ability and cultivation of the scientific inquiry critical to advanced mathematical modeling and problem solving. Foundational ideas of current innovative thinkers lead to music and math educational innovations. The work of Pulitzer Prize winner Douglas Hofstadter drew attention to an interconnectedness of mathematics, symmetry and intelligence in a way that included music and expression.
Howard Gardner’s theory of Multiple Intelligences provided a framework on which to hang some of Hofstadter’s ideas. Gardner’s landmark Frames of Mind: The Theory of Multiple Intelligences (1983) validated how intermingling of academic disciplines at that time maximized learning by appealing to an individual’s own specific learning strengths.
Utilizing aspects of multiple intelligence theory and the effects of creativity, psychologist Mihaly Csikszentmihalyi established states of mind that cognitively join moments of creative expression. He recognized full engagement in an activity to the point of becoming almost lost in the creativity of that moment, reaching something close to a meditative state where perception and interaction with elements of a system flow freely. Strong theoretical arguments and research connecting cognition of music and math made since the initial work of the aforementioned remain viable. Few make use of these connections, so students of our schools merely benefit from concurrent but disjoint studies of math and music.
Much attention however is paid to standardized testing and its effect on rankings among comparable communities. Amid rapid changes to significant aspects of the tests this focus seems short sighted. Frequently it seems that there are more questions about these assessments than there is time to answer them before the next change. Sincere and valid attempts to stay current with instructional practice related to the testing focus and methods are unavoidably one step behind or more as administrators and teachers try their best to prepare students for measurable success.
Even more unfortunate is that very little room remains in a teaching year increasingly dominated by starkly drawn Common Core Standards, imposed pacing and prescribed lesson plans. A system drawn to create measurable outcomes that are easily presented and useful as evaluatory metrics does little to encourage stepping off of the path. Local school boards and school administrators are more than aware what low test scores can mean and that trickles down to teachers. Widespread fear of failure is not uncommon, which in turn stunts creativity and reduces innovation in anything not directly measured by test scores of English, math or science.
Taxpayers certainly deserve mechanisms to indicate how well the schools are doing. It is no secret that public schools cost each resident more than any other taxpayer-funded service and that not all taxpayer households send students to public schools. Training test takers to crank out high scores consequently addresses certain immediate concerns, but often at the expense of the intellectual growth that schools could offer with newer, more substantial, and even more exciting programs.
What is not new in many schools are the high levels of participation in music programs, regardless of the student population’s socio-economic status. Exuberant young students begin their music experience in elementary school and continue to become excellent singers and musicians. All along the way there is pride in performance and appreciation from people of the community. Strong support is easily recognizable, as is respect for music as a field of study. Exemplary music programs often exist alongside dedicated content teachers and math departments ready to explore new approaches to their curricula.
As part of a 2013 study by An, Capraro and Tillman that examined adaptation, design, and implementation, teachers at elementary schools in Southern California developed a music-mathematics interdisciplinary curriculum successfully. Students used notation and played different musical instruments (handbells, drums, music sticks, and keyboards) as manipulatives to learn mathematical strategy, application and modeling. The lessons taught included all of five of the mathematics content areas listed in the 2009 Mathematics Content Standards for California Public Schools, including number sense, algebra and functions, measurement and geometry, statistics, data analysis, probability, and mathematical reasoning.
The Ford Foundation awarded a two-year $150,000 grant in 2007 to Washington State Board for Community and Technical Colleges in support of their program for the integration of the arts and advanced math ideas. This was a result of their Transition Math Project which was funded by the the Washington State Legislature and the Gates Foundation. The result was development of a cross-discipline focus on a wide variety of mathematical topics that connect to artistic projects. Among these are real world applications that bring music to Algebra II, Precalculus, and Trigonometry topics that include function notation, translation of functions, and application/translation of sine functions.
Interactions between teachers can invigorate all involved on the way to establishing ownership of a unique and compelling approach to an old set of ideas. Larger and more heterogeneous groups will allow for interaction among struggling students with those who are successful in either math or music, or both. Because music education already exists, is proven, and is often highly regarded when and where it is successful, revolutionary change is not necessary. Begin by communicating the connections between music and math, or any other discipline. Any steps further forward will increase the benefits.
Established educational connections are hardly limited to music and math, but they are all useless if we fail to acknowledge them. We must see past the dominance of content directly measured by standardized tests; it is our responsibility. Let us take bold steps with faith in real intellectual growth rather than fear of the effects of negative data.
Tony Ryba has been a math teacher for twenty-three years. He is currently studying secondary math education at CCSU.
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